WASHINGTON — Senate Republicans on Thursday killed a measure backed by President Barack Obama that would encourage companies to bring overseas jobs back to the United States.

The measure being pressed by Obama’s Democratic allies is rich with political symbolism, but whether it would have had much practical impact on decisions by companies to “outsource” jobs to lower-wage countries is open to question.

Democrats brought the measure to the Senate floor in concert with political attacks on Mitt Romney, whose private equity firm, Bain Capital, promoted the practice of outsourcing jobs to countries like China and India.

The bill would forbid companies from deducting the expenses of moving workers or operations overseas from the U.S., and would offer a 20 percent credit for the costs of shifting workers back home.

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Republicans blocked the measure on a 56-42 vote that fell just four votes of the 60 required to overcome a filibuster. Most Republicans opposed the measure on its merits, but the GOP opposition was cemented after top Senate Democrat Harry Reid appeared to indicate that he would not permit Republicans to offer amendments to the measure.

Four Republicans voted with Democrats: Olympia Snowe and Susan Collins of Maine; Dean Heller of Nevada; and Scott Brown of Massachusetts.

Sen. Dick Durbin of Illinois, the No. 2 Democrat in the Senate, said the legislation “asks whether we should continue to reward and incentivize American businesses to send jobs overseas to low-wage countries or create incentives for them to bring the jobs back home.”

But the official tax analysts for Congress at the Joint Committee on Taxation said that disallowing the deduction for outsourcing expenses would raise just $14 million next year, which appears to indicate that the measure wouldn’t deter outsourcing very much. The new credit for bringing workers back to the U.S. would cost just $21 million next year. Republican Sen. Orrin Hatch of Utah pointed out that Obama has spent more than that on ads attacking Romney on the issue.

The measure is cosponsored by Democratic Sens. Debbie Stabenow of Michigan and Sherrod Brown of Ohio, who both face re-election this year in states that have witnessed the loss of hundreds of thousands of manufacturing jobs in recent decades.

“We need to be exporting our products, not our jobs,” said Stabenow. “Instead of giving tax breaks to companies that ship jobs overseas, we need to be cutting taxes for U.S. companies that create jobs in America.”

Thursday vote was a precursor to debate next week on extending the Bush-era tax cuts. Most Democrats appear to be sticking with Obama’s position that tax rates on family income exceeding $250,000 should return to Clinton-era levels, with the top rate increasing from 35 percent to 39.6 percent. Republicans want a full one-year extension of all the current rates.

Republicans circulated a new analysis of the competing measures that indicates the $301 billion GOP plan would only cost $29 billion more than a plan circulated by Democrats.

At a recent campaign stop in Ohio, Obama said that the nation doesn’t “need a president who wants to ship more jobs overseas.”

The legislation was opposed by prominent business groups including the U.S. Chamber of Commerce.

The legislation, said Business Roundtable President John Engler in a letter to lawmakers, “would saddle American businesses with new costs not faced by their foreign competitors.”